Pith. sign in

REVIEW 3 major objections 7 minor 1 cited by

Searching for pulsars in Globular Clusters with the Fast Fold Algorithm and a new pulsar discovered in M13

T0 review · 3 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A fast-folding search of 16 globular clusters has found a new 6.37-ms binary pulsar, M13I, and recovered 87 of 93 known pulsars.

desk verdict A solid search paper that finds a genuinely new binary millisecond pulsar in M13 with a credible timing solution; the main caveat is that cluster membership rests on position and DM alone, not proper motion. read the letter →

arxiv 2505.05021 v2 pith:SFXPNH26 submitted 2025-05-08 astro-ph.HE

Yaowei Li , Lin Wang , Lei Qian , Liyun Zhang , Yujie Chen , Dejiang Yin , Baoda Li , Yinfeng Dai
show 10 more authors
Ralph P. Eatough Wenze Li Dongyue Jiang Xingnan Zhang Minghui Li Yujie Lian Yuxiao Wu Tong Liu Kuo Liu Zhichen Pan
This is my paper · ORCID
classification astro-ph.HE
keywords pulsarsglobularclustersFastFoldingAlgorithmmillisecondbinarytelescopeM13timingsolution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that applying the Fast Folding Algorithm (FFA) to L-band observations of globular clusters taken with the Five-hundred-meter Aperture Spherical radio Telescope recovers nearly every known pulsar and can uncover faint signals that Fourier-transform searches miss. On that basis it reports the discovery of M13I (PSR J1641+3624I), a 6.37-ms pulsar in an 18.23-day eccentric binary (e = 0.064) inside the cluster M13, with a phase-coherent timing solution spanning six years. The detection counts (38 of 39 isolated, 49 of 54 binary pulsars) and the new pulsar's orbital properties are the paper's central results. A sympathetic reader would care because the new system occupies a part of orbital-parameter space not previously seen in M13, suggesting an evolutionary path distinct from the cluster's other binary pulsars.

What carries the argument

The central object is the Fast Folding Algorithm (FFA), a time-domain search that folds a dedispersed time series at each trial period and sums the folded profile over the full observation, implemented here in a software package whose search command operates on whitened time series. FFA's sensitivity advantage over FFT is largest for weak signals with long spin periods, and its computational cost scales as the inverse square of the minimum search period, which is why the search adopted cluster-specific minimum periods of 3-50 ms and a period ceiling of 100 s. The paper also uses the detectability condition $|\dot P| \le 2(P/T)^2$ to show that binaries with period derivatives above about $10^{-12}$ s/s accumulate more than one cycle of phase drift in a one-hour fold and therefore evade a fixed-period FFA search, quantitatively explaining the non-detected pulsars.

What would settle it

A proper-motion or parallax measurement of M13I that disagrees with M13's cluster motion would falsify the physical association; alternatively, an independent blind re-reduction of the same FAST observations with a public FFA implementation that fails to reproduce M13I's signal or the reported re-detection counts would falsify the survey result.

Watch

Extended reading notes

Core claim

The paper's central discovery is M13I, a millisecond pulsar with spin period 6.37 ms and dispersion measure 29.58 pc $cm^{-3}$, located 11.7 arcseconds from the center of globular cluster M13. Using 78 FAST observations over six years the authors obtained a phase-coherent timing solution showing an 18.233778-day orbit with eccentricity 0.064356, a projected semi-major axis of 20.71515 light-seconds, and a companion mass between 0.45 and 1.37 solar masses (median 0.54), consistent with a helium white dwarf. The same FFA pipeline re-detected 38 of 39 known isolated pulsars and 49 of 54 known binary pulsars across 16 clusters, with the six non-detections attributed to orbital acceleration, weak signal-to-noise, or use of a known ephemeris. The paper claims that FFA detected M13I in 14 of 78 observations (17.9%) versus 8 of 78 (10.3%) for FFT searches, and that M13I's wide, eccentric orbit breaks the eccentricity-versus-distance trend previously seen among M13 binaries.

Load-bearing premise

That the new pulsar M13I is a member of globular cluster M13, inferred only from sky position (11.7 arcseconds from the center) and dispersion measure (29.58 pc $cm^{-3}$), with no independent distance or proper-motion measurement.

Editorial extensions

If this is right

  • For isolated cluster pulsars, FFA recovery is essentially complete: 38 of 39 were re-detected, so the one failure reflects signal weakness or a stacking-only detection, not a general method gap.
  • The six non-detections are quantitatively explained by the $|\dot P| \le 2(P/T)^2$ criterion, so future FFA searches can predict which binaries will be missed and can schedule shorter integrations or acceleration fits for them.
  • M13I's orbital parameters double the spread of M13 binary pulsars along both period and eccentricity, implying that M13's pulsar population is not a single coeval, tidally circularized family.
  • FFA's higher detection rate on M13I (14 of 78 versus 8 of 78 observations) suggests that reprocessing existing FAST globular-cluster data with FFA, rather than taking new observations, is a viable route to finding more faint pulsars.
  • No new pulsars emerged from 138,448 candidates in 14 clusters with no known pulsars, indicating that any pulsars there are fainter or shorter-period than this search could reach.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If M13I is truly a cluster member, its low dispersion measure places it in the near hemisphere of M13; a future proper-motion or timing-acceleration measurement could test whether its wide eccentric orbit results from a recent dynamical encounter rather than from isolated binary evolution.
  • The inverse-square cost scaling implies that a rerun of the same pipeline with the minimum search period lowered to 1-2 ms, when computing budgets allow, could reveal sub-3-ms pulsars that the current search's harmonic-only sensitivity missed.
  • Extending the same FFA approach to FAST archival data for other globular clusters beyond the 30 studied here is a natural next step and could be done without new telescope time.
  • Adding an acceleration-search stage to the FFA pipeline would likely recover the five high-acceleration binaries missed here, closing most of the completeness gap.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper reports an FFA-based pulsar search of 16 globular clusters observed with FAST, using the RIPTIDE package. The pipeline re-detects 38/39 isolated and 49/54 binary pulsars among previously known sources, with non-detections attributed to orbital acceleration or low SNR. The main result is the discovery of M13I (PSR J1641+3627I), a 6.37 ms binary millisecond pulsar in M13, with a six-year phase-coherent timing solution yielding an 18.23-day orbit, eccentricity 0.064, and companion mass 0.45-1.37 Msun. The paper also compares FFA and FFT detection rates for M13I, reports a computational speed comparison, and discusses the pulsar's orbital properties as evidence for a distinct evolutionary path.

Significance. The discovery of M13I is a valuable addition to the known pulsar population in globular clusters, and the timing solution appears robust, with 68 ToAs and 53 us RMS residuals. The re-detection statistics provide a useful benchmark for FFA pipelines on FAST data. If the cluster membership is confirmed, the system's long orbital period and moderate eccentricity make it an interesting test case for binary evolution in dense cluster environments. The work also demonstrates the practical feasibility of FFA searches on FAST's high-rate data, which is relevant for future surveys. However, the significance of the evolutionary interpretation is conditional on the assumed cluster membership and on the validity of the FFA-vs-FFT comparison.

major comments (3)
  1. [Section 3.2 and Section 4.3] The physical association of M13I with the globular cluster M13 is asserted from the 11.7 arcsec angular offset and DM = 29.58 pc cm^-3 lying within the 27-34 pc cm^-3 range in Table 1, but no proper-motion measurement, parallax, or statistical chance-coincidence estimate is presented. This assumption is load-bearing: the title and abstract call M13I a pulsar 'in M13', and Section 4.3 uses the DM to place it in the nearer cluster hemisphere and uses the eccentricity to claim a contradiction with the Wang et al. (2020) trend. I request either a quantitative estimate of the probability that a field pulsar with this DM falls within 11.7 arcsec of the cluster center, or a proper-motion constraint from the 6-year timing data. At minimum, the wording in Section 4.3 should distinguish between the measured timing parameters and the assumed cluster membership.
  2. [Section 4.1 and Figure 4] The paper claims that FFA detected M13I in 14 of 78 observations (17.9%) versus 8 of 78 (10.3%) for FFT, and Section 5 concludes that 'FFA demonstrates superior sensitivity to weakly accelerated signals.' However, the FFT search parameters are not specified: no harmonic-summing setting, acceleration-search zmax, period range, DM step, or SNR threshold is given for the comparison. Without a controlled setup, the 1.75x factor may reflect differences in search configuration rather than algorithmic sensitivity. Please state the exact FFT pipeline used (or clarify that the comparison is against archival PRESTO processing with a specific configuration) and temper the conclusion to a statement about this dataset. If a controlled comparison is not feasible, the sentence in the conclusion should be revised.
  3. [Section 4.1, detectability condition] The explanation for the non-detection of M12B and M13H states that their period derivatives 'exceed 10^-11 s/s, far above the detectability threshold' derived from |\dot{P}| ≤ 2(P/T)^2. For M13H, P = 11.21 ms and T = 1 hour give a threshold of approximately 1.9×10^-11 s/s, so a value just above 10^-11 is not 'far above.' Please report the actual measured \dot{P} values (or at least their order of magnitude) for both pulsars, or rephrase the statement to be quantitatively accurate for each object.
minor comments (7)
  1. [Section 3.2] The pulsar designation is inconsistent: the abstract gives PSR J1641+3627I, Section 3.2 gives J1641+3624I, and Table 3 coordinates (Dec +36:27:36.5) support the former. Please correct.
  2. [Section 3.1 and Table 1] Table 1 lists 9 known pulsars in M13 and 8 FFA detections, but the text in Section 3.1 says 93 known pulsars were analyzed, before the discovery of M13I. Please clarify whether the table includes the new pulsar and reconcile the total count.
  3. [Section 3.2, first paragraph] The statement that M13I was 'initially overlooked in earlier searches' is followed by the report of a single-day archival PRESTO detection; please clarify whether that detection was previously recognized as a pulsar or only in hindsight.
  4. [Section 4.1, M14D/M14E] The text first attributes their non-detection to weak signals (SNR<7 after coherent folding) and then to 'significant orbital acceleration effects'; please reconcile these explanations or state which is dominant.
  5. [Section 4.2] The speed comparison uses accelsearch with zmax=0, i.e., no acceleration search, while rffa is a full folding search; this is not a like-for-like benchmark and should be stated as a limitation.
  6. [General] There are numerous typographical and grammatical errors, including 'puslars', 'de-dispered times series', 'redetectining', 'summerized', 'highghting', and 'privious'. A careful proofread is needed.
  7. [References] The two Losovsky & Dumsky 2014 entries appear to refer to the same work with different author-name formatting; merge or disambiguate them.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: M13I is a measured timing solution validated by external re-detection benchmarks.

full rationale

The paper's central new result is an observational discovery and a timing fit. The FFA pipeline is validated against 93 known pulsars in 16 clusters; detecting 38 of 39 isolated and 49 of 54 binary pulsars is an external benchmark, not a fitted prediction, because the search is blind in period and the known pulsars were not used to train the detection criterion. The M13I timing solution (spin, orbital period, eccentricity, companion mass range) is obtained by standard ToA fitting with TEMPO; no parameter is defined as the output of the fit and then claimed as an independent prediction. The only potentially load-bearing interpretive step is the cluster association of M13I, which rests on an 11.7 arcsec projected offset from the cluster center and DM = 29.58 pc cm^-3 being inside the 27-34 pc cm^-3 range. That is an evidence-weighting assumption rather than a circular derivation: the pulsar's discovery and timing parameters are measured independently of the membership label, and no equation in the paper reduces the membership conclusion to the fitted parameters or to a self-citation. Self-citations to prior FAST survey papers provide context and comparison data, but the discovery and timing solution stand on the present observations. Hence the derivation chain is self-contained and no significant circularity is present.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

No new physical entities are postulated. The free-parameter set is empty because the pulsar's spin and orbital parameters are measured from the data rather than introduced to force a conclusion.

assumptions (3)
  • domain assumption M13I is associated with globular cluster M13 based on sky position and dispersion measure.
    Section 4.3 uses DM 29.58 pc/cc as membership evidence; no independent distance measurement.
  • domain assumption The companion mass range is computed assuming a neutron star mass of 1.4 solar masses and random orbital inclination.
    Table 3 note states masses are calculated assuming a pulsar mass of 1.4 solar masses.
  • domain assumption The detectability condition for accelerated pulsars assumes constant line-of-sight acceleration over each observation.
    Section 4.1 derives |Pdot| <= 2(P/T)^2 using a quadratic phase model with constant acceleration.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Searching for pulsars in Globular Clusters with the Fast Fold Algorithm and a new pulsar discovered in M13." pith.science (2026). https://pith.science/paper/SFXPNH26

@misc{pith2026250505021,
  author       = {Pith},
  title        = {Pith review of: Searching for pulsars in Globular Clusters with the Fast Fold Algorithm and a new pulsar discovered in M13},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SFXPNH26}},
  note         = {Machine review of arXiv:2505.05021}
}
abstract

We employed the Fast Folding Algorithm (FFA) on L-Band Globular Cluster (GC) observations taken with Five-hundred-meter Aperture Spherical radio Telescope (FAST) to search for new pulsars, especially those with a long rotational period. We conducted a search across 16 GCs that collectively host 93 known pulsars, as well as 14 GCs that do not contain any known pulsars. The majority of these known pulsars were successfully re-detected in our survey. The few non-detections could be attributed to the high accelerations of these pulsars. Additionally, we have discovered a new binary millisecond pulsar, namely M13I (or PSR J1641+3627I) in GC M13 (or NGC 6205), and obtained its phase-coherent timing solution using observations spanning 6 years. M13I has a spin period of 6.37 ms, and an orbital period of 18.23 days. The eccentricity of the binary orbit is 0.064, with a companion mass range of approximately 0.45 to 1.37 M$_{\odot}$. The orbital properties of M13I are remarkably different from those of the other known pulsars in M13, indicating that this pulsar has undergone a different evolutionary path compared to the rest.

Figures

Figures reproduced from arXiv: 2505.05021 by the authors.

Figure 1
Figure 1. The discovery plot of M13I. The observation date is January 23, 2023. The lower part of the plot shows the candidate plot generated by RIPTIDE, while the upper part displays the folded plot of the same signal using PRESTO [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. The left and right of the plot are the time residuals from the best-fit timing model and the timing residuals as a function of orbital phase for the M13I, respectively [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. The plot shows the polarization calibrated pulse profile of M13I measured at FAST in 2023 - MJD 59966 (the black line represent the total polarization profile, the red line represent the linear polarization profile, and the blue line represent the circular polarization profile).The PA are shown in the upper panel [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: A plot showing the time taken for FFA and accelsearch with different data lengths. The values 3 ms, 10 ms, 50 ms, and 100 ms represent the minimum search periods set for the FFA searches, and accelsearch refers to the search conducted using PRESTO. 4.3. Properties of t…
Figure 4
Figure 4. Figure 4: A plot of SNR comparison of M13I detections by FFA and FFT. Green circles denote FFA detections (14 instances in total), while red squares represent FFT detec￾tions (8 instances). The FFT exhibited a higher SNR than FFA only on the day with the strongest signal, wherea…
Figure 6
Figure 6. Figure 6: Relation between orbital period and eccentricity of pulsars in GCs. Blue dots are binary pulsars in GCs (ex￾cept M13), red triangles are privious known binary pulsars in M13 (B,D,E and F), and the star represents M13I. Data from website 1. 5. CONCLUSION We conducted a …

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The FAST Globular Cluster Pulsar Survey (GC FANS)

    astro-ph.HE 2025-06 conditional novelty 6.0 of 10

    The FAST globular cluster pulsar survey reports 60 new pulsars and identifies M71D as a likely double neutron star system formed through standard massive binary evolution.

Reference graph

Works this paper leans on

35 extracted references · 4 canonical work pages · cited by 1 Pith paper

  1. [1]

    R., Devour, B

    Crawford, F., Lorimer, D. R., Devour, B. M., Takacs, B. P., & Kondratiev, V. I. 2009, ApJ, 696, 574, doi: 10.1088/0004-637X/696/1/574

    work page doi:10.1088/0004-637x/696/1/574 2009

  2. [2]

    2020, ApJL, 888, L18, doi: 10.3847/2041-8213/ab621a

    Dai, S., Johnston, S., Kerr, M., et al. 2020, ApJL, 888, L18, doi: 10.3847/2041-8213/ab621a

    doi:10.3847/2041-8213/ab621a 2020

  3. [3]

    V., Ransom, S

    Douglas, A., Padmanabh, P. V., Ransom, S. M., et al. 2022, ApJ, 927, 126, doi: 10.3847/1538-4357/ac4744

    doi:10.3847/1538-4357/ac4744 2022

  4. [4]

    Freire, P. C. C., Ridolfi, A., Kramer, M., et al. 2017, MNRAS, 471, 857, doi: 10.1093/mnras/stx1533

    doi:10.1093/mnras/stx1533 2017

  5. [5]

    Harris, W. E. 1996, AJ, 112, 1487, doi: 10.1086/118116

    doi:10.1086/118116 1996

  6. [6]

    C., & Rasio, F

    Heggie, D. C., & Rasio, F. A. 1996, MNRAS, 282, 1064, doi: 10.1093/mnras/282.3.1064

    doi:10.1093/mnras/282.3.1064 1996

  7. [7]

    W., van Straten, W., & Manchester, R

    Hotan, A. W., van Straten, W., & Manchester, R. N. 2004, Publications of the Astronomical Society of Australia, 21, 302–309, doi: 10.1071/as04022

    doi:10.1071/as04022 2004

  8. [8]

    2019, Science China

    Jiang, P., Yue, Y., Gan, H., et al. 2019, Science China

    2019

Show all 35 references
  1. [9]

    Physics, Mechanics, and Astronomy, 62, 959502, doi: 10.1007/s11433-018-9376-1

    doi

  2. [10]

    2020, Research in Astronomy and Astrophysics, 20, 064, doi: 10.1088/1674-4527/20/5/64

    Jiang, P., Tang, N.-Y., Hou, L.-G., et al. 2020, Research in Astronomy and Astrophysics, 20, 064, doi: 10.1088/1674-4527/20/5/64

    2020 doi

  3. [11]

    M., & Kulkarni, S

    Johnston, H. M., & Kulkarni, S. R. 1991, ApJ, 368, 504, doi: 10.1086/169715

    1991 doi

  4. [12]

    I., McLaughlin, M

    Kondratiev, V. I., McLaughlin, M. A., Lorimer, D. R., et al. 2009, ApJ, 702, 692, doi: 10.1088/0004-637X/702/1/692 12

    2009 doi

  5. [13]

    2024, ApJ, 972, 43, doi: 10.3847/1538-4357/ad5a82

    Li, B., Zhang, L.-y., Yao, J., et al. 2024, ApJ, 972, 43, doi: 10.3847/1538-4357/ad5a82

    2024 doi

  6. [14]

    R., & Kramer, M

    Lorimer, D. R., & Kramer, M. 2005, Handbook of pulsar astronomy, Vol. 4 (Cambridge university press)

    2005

  7. [15]

    2014, in 40th COSPAR Scientific Assembly, Vol

    Losovsky, B., & Dmitry Dumsky, M. 2014, in 40th COSPAR Scientific Assembly, Vol. 40, E1.15–32–14

    2014

  8. [16]

    Y., & Dumsky, D

    Losovsky, B. Y., & Dumsky, D. V. 2014, Astronomy Reports, 58, 537, doi: 10.1134/S1063772914080034

    2014 doi

  9. [17]

    Lyne, A. G. 2020, MNRAS, 497, 4654, doi: 10.1093/mnras/staa2291

    2020 doi

  10. [18]

    2011, International Journal of Modern Physics D, 20, 989, doi: 10.1142/S0218271811019335

    Nan, R., Li, D., Jin, C., et al. 2011, International Journal of Modern Physics D, 20, 989, doi: 10.1142/S0218271811019335

    2011 doi

  11. [19]

    M., Lorimer, D

    Pan, Z., Ransom, S. M., Lorimer, D. R., et al. 2020, ApJL, 892, L6, doi: 10.3847/2041-8213/ab799d

    2020 doi

  12. [20]

    2021a, ApJL, 915, L28, doi: 10.3847/2041-8213/ac0bbd

    Pan, Z., Qian, L., Ma, X., et al. 2021a, ApJL, 915, L28, doi: 10.3847/2041-8213/ac0bbd

    doi

  13. [21]

    2021b, Research in Astronomy and Astrophysics, 21, 143, doi: 10.1088/1674-4527/21/6/143

    Pan, Z., Ma, X.-Y., Qian, L., et al. 2021b, Research in Astronomy and Astrophysics, 21, 143, doi: 10.1088/1674-4527/21/6/143

    doi

  14. [22]

    G., Jiang, P., et al

    Pan, Z., Lu, J. G., Jiang, P., et al. 2023, Nature, 620, 961, doi: 10.1038/s41586-023-06308-w

    2023 doi

  15. [23]

    M., Ransom, S

    Parent, E., Kaspi, V. M., Ransom, S. M., et al. 2018, ApJ, 861, 44, doi: 10.3847/1538-4357/aac5f0

    2018 doi

  16. [24]

    Phinney, E. S. 1992, Philosophical Transactions of the Royal Society of London Series A, 341, 39, doi: 10.1098/rsta.1992.0084

    1992

  17. [25]

    M., Eikenberry, S

    Ransom, S. M., Eikenberry, S. S., & Middleditch, J. 2002, AJ, 124, 1788, doi: 10.1086/342285

    2002 doi

  18. [26]

    Ridolfi, A., Gautam, T., Freire, P. C. C., et al. 2021, MNRAS, 504, 1407, doi: 10.1093/mnras/stab790

    2021 doi

  19. [27]

    Staelin, D. H. 1969, IEEE Proceedings, 57, 724, doi: 10.1109/PROC.1969.7051

    1969

  20. [28]

    W., Bailes, M., et al

    Vleeschower, L., Stappers, B. W., Bailes, M., et al. 2022, MNRAS, 513, 1386, doi: 10.1093/mnras/stac921

    2022 doi

  21. [29]

    W., et al

    Wang, L., Peng, B., Stappers, B. W., et al. 2020, ApJ, 892, 43, doi: 10.3847/1538-4357/ab76cc

    2020 doi

  22. [30]

    F., Han, J

    Wang, P. F., Han, J. L., Xu, J., et al. 2023, Research in Astronomy and Astrophysics, 23, 104002, doi: 10.1088/1674-4527/acea1f

    2023 doi

  23. [31]

    2024, ApJL, 974, L23, doi: 10.3847/2041-8213/ad7b9e

    Wu, Y., Pan, Z., Qian, L., et al. 2024, ApJL, 974, L23, doi: 10.3847/2041-8213/ad7b9e

    2024 doi

  24. [32]

    M., Manchester, R

    Yao, J. M., Manchester, R. N., & Wang, N. 2017, ApJ, 835, 29, doi: 10.3847/1538-4357/835/1/29

    2017 doi

  25. [33]

    2024, ApJL, 969, L7, doi: 10.3847/2041-8213/ad534e

    Yin, D., Zhang, L.-y., Qian, L., et al. 2024, ApJL, 969, L7, doi: 10.3847/2041-8213/ad534e

    2024 doi

  26. [34]

    2024, Science China

    Zhou, D., Wang, P., Li, D., et al. 2024, Science China

    2024

  27. [35]

    Physics, Mechanics, and Astronomy, 67, 269512, doi: 10.1007/s11433-023-2362-x

    doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.